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Variational inference for Bayesian panel VAR models

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  • Ter Steege, Lucas

Abstract

We study the application of approximate mean field variational inference algorithms to Bayesian panel VAR models in which an exchangeable prior is placed on the dynamic parameters and the residuals follow either a Gaussian or a Student-t distribution. This reduces the estimation time of possibly several hours using conventional MCMC methods to less than a minute using variational inference algorithms. Next to considerable speed improvements, our results show that the approximations accurately capture the dynamic effects of macroeconomic shocks as well as overall parameter uncertainty. The application with Student-t residuals shows that it is computationally easy to include the COVID-19 observations in Bayesian panel VARs, thus offering a fast way to estimate such models. JEL Classification: C18, C32, C33

Suggested Citation

  • Ter Steege, Lucas, 2024. "Variational inference for Bayesian panel VAR models," Working Paper Series 2991, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20242991
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    References listed on IDEAS

    as
    1. Chan, Joshua C.C. & Yu, Xuewen, 2022. "Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    2. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2023. "Forecasting using variational Bayesian inference in large vector autoregressions with hierarchical shrinkage," International Journal of Forecasting, Elsevier, vol. 39(1), pages 346-363.
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    6. Bobeica, Elena & Hartwig, Benny, 2023. "The COVID-19 shock and challenges for inflation modelling," International Journal of Forecasting, Elsevier, vol. 39(1), pages 519-539.
    7. Reza Hajargasht, 2019. "Approximation Properties of Variational Bayes for Vector Autoregressions," Papers 1903.00617, arXiv.org.
    8. Hartwig, Benny, 2022. "Bayesian VARs and prior calibration in times of COVID-19," Discussion Papers 52/2022, Deutsche Bundesbank.
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    More about this item

    Keywords

    panel-VAR; student-t distribution; variational Bayes;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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